LETTERSPUBLISHED ONLINE: 20 FEBRUARY 2011 | DOI: 10.1038/NGEO1083

Reconciling the hemispherical structure of Earth’sinner core with its super-rotationLaurenWaszek*, Jessica Irving and Arwen Deuss

Earth’s solid inner core grows through solidification of materialfrom the fluid outer core onto its surface at rates of about 1 mmper year1, freezing in core properties over time and generatingan age–depth relation for the inner core. A hemisphericalstructure of the inner core is well-documented: an isotropiceastern hemisphere with fast seismic velocities contrasts witha slower, anisotropic western hemisphere2–4. Independently,the inner core is reported to super-rotate at rates of up to 1◦

per year5–7. Considering the slow growth, steady rotation ratesof this magnitude would erase ’frozen-in’ regional variation andcannot coexist with hemispherical structure. Here, we exploitthe age–depth relation, using the largest available PKIKP–PKiKP seismic travel time data set, to confirm hemisphericalstructure in the uppermost inner core, and to constrain thelocations of the hemisphere boundaries. We find consistenteastward displacement of these boundaries with depth, fromwhich we infer extremely slow steady inner core super-rotationof 0.1◦–1◦ per million years. Our estimate of long-term super-rotation reconciles inner core rotation with hemisphericalstructure, two properties previously thought incompatible. It isin excellent agreement with geodynamo simulations8,9, whilenot excluding the possibility that the much larger rotationrates inferred earlier5–7 correspond to fluctuations in inner corerotation on shorter timescales10.

The Earth’s solid inner core was first discovered by theobservation of PKiKP, a seismic wave which travels through themantle and outer core before reflecting from the sharp inner coreboundary (ICB; ref. 11). The inner core is composedmostly of iron,growing through solidification of outer core material onto the ICBsurface as the Earth cools, resulting in deeper structure being older.Although the thermal history of the inner core is debated12,13, itsuppermost structure results from processes occurring in the recentpast, of which we have greatest understanding; these mechanismsare unlikely to have changed in the last 100Myr. This resultingtime–depth variation of the upper inner core is key to investigatingany changing environment at the ICB region associated withinner core super-rotation.

Hemispherical variation in the velocity, anisotropy andattenuation structure of the upper inner core have been investigatedrepeatedly and, although there is still much uncertainty regardingthe detailed characteristics, these properties are consistentlyreported in previous studies2,14,15. Velocity anisotropy wasoriginally determined as present throughout the entire inner core,through both body-wave and normal-mode observations16–18.Following these discoveries, a layered structure was found in theuppermost inner core: an isotropic layer of debated thicknessatop deeper anisotropic structure3,19. Concurrent investigationsobserve large regional differences: strong anisotropy in thewestern hemisphere, with little to none in the east4,20,21. Theeastern hemisphere shows a higher velocity than the western

Bullard Laboratories, Department of Earth Sciences, University of Cambridge, CB3 0EZ, UK. *e-mail: lw313@cam.ac.uk.

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Figure 1 | Ray paths, travel time curves and an example of the seismicphases PKIKP and PKiKP. a, Ray paths of PKIKP (blue) and PKiKP (red) foran event at 100 km depth. b, Travel time curves of PKIKP and PKiKP. Theearthquake–receiver epicentral distance range of 130◦–143◦ avoids bothinteraction between the phases and interference from the outer coresensitive phase PKP (black). c, A seismogram from the Peru event of 5September 2009, station AAK, epicentral distance 139◦. PKiKP arrives justunder 2 s later than PKIKP with opposite polarity and a slightlylarger amplitude.

hemisphere22; these differences are present to depths of atleast 800 km (ref. 23).

Several mechanisms have been proposed as responsible forimprinting texture which results in hemispherical structure. It hasbeen suggested to arise from thermochemical coupling of the innercore with the core–mantle boundary (CMB) region8, in whichmoreheat is extracted in the eastern hemisphere, creating a localizedincrease in inner core growth rate. This variation in freezing ratesmay also explain seismic texture throughout the inner core. Morerecent studies propose that the differences are a consequence ofmelting in the eastern hemisphere and freezing in the west, resultingin a lateral translation of the inner core eastwards12,13.

Here, the uppermost inner core is studied with PKIKP, whichtravels through the Earth’s mantle, outer core, and inner core, anda reference phase PKiKP, which has a similar path but reflects offthe ICB (Fig. 1a). PKIKP and PKiKP can be observed as individualarrivals for earthquake–receiver epicentral distances of 130◦–143◦(Fig. 1b), whereby PKIKP samples up to approximately 90 kmdeep into the inner core. From every suitable event between 1990and 2010, a total of 2,497 acceptable seismograms were obtained,making this the most extensive PKIKP–PKiKP study to date.

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NATURE GEOSCIENCE DOI: 10.1038/NGEO1083 LETTERS

West East

¬1.0 ¬0.5 0 0.5 1.0

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Figure 2 |Map showing all PKIKP–PKiKP differential travel time residual data collected. Thin lines indicate PKIKP ray paths through the inner core, andthe locations of the circles correspond to the turning points of the rays. A clear hemispherical difference can be observed, with predominantly positiveresiduals (red circles) in the east due to faster velocity structure here, and negative residuals (blue circles) in the west indicating slower velocity.Hemisphere boundaries as a function of ray turning depth are indicated: Solid line 39–52 km, dashed line 52–67 km, and dotted line 67–89 km belowthe ICB.

Arrival times of the phases are picked using cross-correlation andhand-picking techniques (Fig. 1c). The PKIKP–PKiKP differentialtravel time is compared with that predicted by the seismic referencemodel AK135 (ref. 24) to obtain the PKIKP–PKiKP residuals.The paths of these two phases diverge only at the top of theinner core, thus any variation in the differential travel timeresiduals indicates a departure in inner core velocity structure fromthe 1D Earth model.

Our data set confirms that the velocity structure of theupper inner core comprises two distinct eastern and westernhemispheres (Fig. 2). Positive travel time residuals (shown asred circles) in the eastern hemisphere indicate faster veloc-ity structure than AK135, whereas the west contains mostlynegative residuals (blue circles) and hence is slower than themodel. Also present in the western hemisphere are faster paths(red circles) orientated in the polar, north–south, direction.Polar paths have ζ < 35◦, where ζ is the angle betweenthe PKIKP ray path in the inner core and Earth’s rotationaxis. These paths have residual values comparable to thosein the eastern hemisphere, and reveal anisotropy aligned withEarth’s rotation axis, in good agreement with known anisotropicstructure17,18 (Supplementary Fig. SI1). Similar anomalous polartravel time residuals are not observed in the east, indicatingisotropic velocity structure.

Previous studies have not led to well-defined limits on thelongitude of the hemisphere boundary locations, which range from40◦ to 60◦ for the eastern boundary, and from 160◦ to 180◦ for thewestern boundary2,3,21. The uncertainty may be due to lack of dataor uneven sampling; this is avoided here through our considerablylarger data set, which provides extensive coverage to constrain theboundaries to the most accurate locations yet.

To explore the temporal changes in the upper inner core wepartition the data by PKIKP turning depth below the ICB. Weseparate the residuals into three turning depth ranges: 39–52 km,52–67 km and 67–89 km below the ICB (Fig. 3). The westernhemisphere (blue data points) has predominantly negative residualsand the eastern hemisphere (red data points) has positive residuals.The hemisphere boundaries are determined to be located at thelongitudes (or range of longitudes) which separate the negative andpositive residuals. Some of the boundaries are constrained by onlyone or two data points, which have been checked for accuracy;the corresponding seismograms for all points which constrain theboundaries are contained in Supplementary Fig. SI2, in which theclarity of the phases can be clearly observed.

Anisotropy in the deep western hemisphere results in positiveresiduals for polar paths, which may then be erroneously identifiedas sampling the eastern hemisphere. To prevent misinterpretation,we omit from Fig. 3 all western polar paths with PKIKP turningpoints deeper than 69 km below the ICB when we determine thehemisphere boundary locations, relying solely on paths with ζ >35◦at this depth. As negligible anisotropy is observed in the easternhemisphere, and serves tomake the residualsmore positive, we neednot remove any points from the east.

We find that both boundaries separating the hemispheres exhibita consistent eastward shift with increasing depth (Fig. 3). Thechange in hemisphere boundary locations with depth are listed inTable 1, and correspond to an average shift of∼20◦ over the 50 kmthick layer. If the inner core rotates faster than the mantle, andhemisphere differences result from frozen-in structure at the ICB,then it is expected that the location of these boundaries will changeover time. The eastward shift of the hemisphere boundaries withdepth may be explained by an eastward displacement of the ICB

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO1083

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Figure 3 | PKIKP–PKiKP differential travel time residuals as a function ofPKIKP turning point longitude, separated according to PKIKP turningdepth. a, 39–52 km below the ICB. b, 52–67 km. c, 67–89 km. Anomalousanisotropic polar paths in the west are omitted. Vertical dashed linesindicate the hemisphere boundaries, which are determined as the longitudewhere the travel time residuals change from predominantly negative topositive. Red points and blue points represent eastern hemisphere andwestern hemisphere data respectively. With increasing depth, theboundaries show a consistent westward shift.

over time, entrained by a very slow steady rotation of the innercore. Thermal evolution investigations calculate the age of the innercore as between 1.0 and 3.6Gyr, the most likely value being atthe younger end of this range25,26. Assuming uniform growth, the∼50 km layer of inner core sampled takes up to 150Myr to grow.Taking the possible shifts of 12◦–29◦ to have occurred over this time,this equates to an extremely slow steady inner core super-rotationof 0.1◦–1◦Myr−1 (Table 1).

Most recently, temporal changes of the inner core structure havebeen explored using either scattering27 or doublet earthquakes6,7,events occurring in the same location with similar mechanismsbut separated in time by a period of up to a few decades. As aresult, steady inner core super-rotation rates of 0.1◦–1.0◦ yr−1 havebeen proposed5–7,27. However, these seismic studies provide onlya snapshot of the current inner core super-rotation. Consideringthe slow growth of the inner core, rotation rates of this magnitudewould completely erase any regional differences frozen in bythe evolving environments at the ICB; this is incompatible withour observations of hemispherical structure. Conversely, normal-mode studies and other body-wave investigations find little to norotation28,29. Our observed steady rotation rate of 0.1–1◦Myr−1 isfar too slow for any doublet earthquake to observe. This suggeststhat previously observed rapid temporal changes of the inner coremay be a result of fluctuations occurring on timescales too shortto allow freezing-in of the properties, including the movement ofsmall scale topography at the inner core surface6, a layered mosaicstructure comprising patches of solid and fluid30, or short timescalefluctuations in inner core rotation9,10.

Examining hemisphere boundaries, a recent normal-modestudy4 finds transition zones between the hemispheres, rather thansharp boundaries, located in approximately the correct vicinity werethe eastward shift to continue with depth. These indistinct locationsmay result from a depth-average of the shifting boundaries.Body-wave investigations in the same study locate the hemisphereboundaries using anisotropy within a depth range of 170–1,090 kmbelow the ICB, finding values of −151◦ ± 61◦ and 14◦ ± 34◦;the large error bounds are compatible with a further eastwardshift with depth. The study uses the anisotropy of the westernhemisphere to locate the boundaries, whereas here we use thedifference in isotropic velocity structure. The isotropic velocitystructure at the top of the inner core is most likely frozen in atthe ICB. Anisotropy only appears at a depth of 69 km below theICB, indicating that anisotropy could result from texturing aftersolidification, and therefore the isotropic velocity and anisotropystructures may not coincide.

Geodynamo simulations which combine the effects ofgravitational coupling of the inner core to the lower mantle withviscomagnetic torques find a small differential rotation of a fewdegrees permillion years9. Themuch faster rotation rates inferred inother seismic studies5–7 may then be a result of inner core oscillationor fluctuations on shorter timescales (∼100 yr), superimposedon this much slower, steady rotation10. Compared with previousseismic observations, our rotation rate of 0.1◦–1◦Myr−1 is muchmore consistent with the geodynamo calculations; the slower ratewould permit the freezing in of regional structure at the ICB.This may be generated from asymmetrical heat flows at the CMB,and subsequent faster growth rates in the eastern hemisphere8.Conversely the hemispheres may arise from convection within theinner core, resulting in melting in the eastern hemisphere andfreezing in the west, accompanied by an eastward lateral translationof the entire inner core12,13. The proposed eastward translation ofthe inner core in addition to steady super-rotation might result inan eastward shift with depth of the boundaries; we find that the eastboundary experiences a greater shift than the west (∼27◦ compared

Table 1 | Longitude of the hemisphere boundary locations with increasing depth below the ICB.

Depth below ICB (km) West boundary East boundary Average eastward shiftwith respect to upper layer

Inner core rotation rate forgrowth rate 0.3mmyr−1

39–52 −173◦ 8◦ to 14◦ – –52–69 −169◦ to−160◦ 21◦ 9◦±6◦ 0.1±0.07◦Myr−1

69–89 −161.5◦ 35◦ to 41◦ 22.25◦± 10.75◦ 0.15±0.07◦Myr−1

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NATURE GEOSCIENCE DOI: 10.1038/NGEO1083 LETTERSwith ∼11.5◦), in good agreement with this idea. However, furthermodelling is required to conclusively reconcile these twoproperties.

As our inner core super-rotation rates is derived from theobserved constant shift of hemisphere boundaries with depth, theobserved hemispherical structure is inherently compatible with thisextremely slow steady rotation. Furthermore, our observation doesnot rule out the possibility of short timescale oscillations or wobblesof the inner core, superimposed on a much slower, steady super-rotation9,10, nor does it exclude the possibility of a lateral translationof the inner core in addition to steady rotation and oscillations12,13.

MethodsThe ideal event to obtain robust PKIKP–PKiKP travel time residuals mustgenerate observable PKIKP and PKiKP phases, well separated both from eachother and their crustal reflections. This criteria requires impulsive ruptures, with5.2<Mw < 6.3, and a source depth of greater than 15 km. Broadband verticalseismic data was filtered between 0.7 and 2.0Hz to centre on the dominantphase frequency of 1.0Hz. A total of 1,162 events were used, resulting in 38,361seismograms before processing.

Received 7 October 2010; accepted 13 January 2011;published online 20 February 2011

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AcknowledgementsThe research was funded by the European Research Council under the EuropeanCommunity’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreementnumber 204995. We thank M. Dumberry and V. Cormier for their constructiveand helpful comments.

Author contributionsL.W. compiled and analysed the data and produced the manuscript and figures. J.I. wrotethe cross-correlation code. J.I. and A.D. supervised the analysis. All authors discussed theresults and implications at all stages.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper on www.nature.com/naturegeoscience. Reprints and permissionsinformation is available online at http://npg.nature.com/reprintsandpermissions.Correspondence and requests formaterials should be addressed to L.W.

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